I'm wondering when should we choose a screwdriver.
Can it be used to put screws in wood, concrete or metal without drilling a hole?
If we need to drill a pilot hole anyway, why don't we just use drills to put the screws in?

When working in cramped spaces, a drill/driver often can't fit. Screwdrivers come in flexible, stubby, right-angle, etc. varieties for such occasions.

For emergencies or odd jobs. Multi-bit screwdriver tools are dirt-cheap now. I have one in all my vehicles. I keep one in my briefcase, one at my grandmother's house, etc. You'd be surprised how often something needs to get screwed ;) and I certainly don't have dozens of cordless drills and chargers.

When the environment is likely to damage an electric device -- working in the rain, or in the mud under a house, or in a very gritty environment, etc. (Note that this is one more reason to make employees buy their own tools.)

When working with a material where finish is important. A driver is much more likely to strip the screw interface, or to slip and mar the material being screwed, or to drive the screw too deep and crack or warp the surface of the material.

When driving slot-head screws. These are notoriously hard to drive with a drill; the bit flies out of the slot too easily.

When a precise torque is needed. (NEVER trust the torque setting on a motorized driver unless it is one of the industrial models made for that purpose and it has been recently calibrated.)

Thanks, @ratchetfreak, I rolled your addition into the answer, if you don't mind.
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Brock AdamsApr 20 '12 at 20:58

2

I want to a see a regular sized screwdriver with a motor and just enough juice for 2-3 screws. A hip holster has a larger battery, so every time you put the driver in, it recharges in a few seconds.
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Jay BazuziApr 20 '12 at 21:13

Your answer is too comprehensive for me to add another, but here's one more case: when you need to unscrew something that's been in place for a long time; power drivers usually just rip the head up or (for adjustable torque) whine quietly.
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kdgregoryApr 21 '12 at 12:36

I like driving a few screws by hand once in a while because it's an incredible forearm workout (in case you're seeking more purpose in your exercise regime). At least with wood; I've never tried concrete.

After years of screwdriver, wrench, and other hand tool use, it's not uncommon to develop Tennis Elbow or Arthritic type conditions. Hand tools are great, but if you are using them constantly throughout your career it might be beneficial to use a power tool from time to time.
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Tester101♦Apr 20 '12 at 13:22

1

the screwdriver is perhaps one of the least ergonomic tools in the toolbox it seems.
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DA01Apr 20 '12 at 16:32

Agreed; it's probably a terrible idea to do it all the time. Edited the answer to be a little more responsibly worded :)
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kwakmunkeeMay 8 '12 at 23:42